We present a method for balancing between the Local and Global Structures
(LGS) in graph embedding, via a tunable parameter. Some embedding methods aim
to capture global structures, while others attempt to preserve local
neighborhoods. Few methods attempt to do both, and it is not always possible to
capture well both local and global information in two dimensions, which is
where most graph drawing live. The choice of using a local or a global
embedding for visualization depends not only on the task but also on the
structure of the underlying data, which may not be known in advance. For a
given graph, LGS aims to find a good balance between the local and global
structure to preserve. We evaluate the performance of LGS with synthetic and
real-world datasets and our results indicate that it is competitive with the
state-of-the-art methods, using established quality metrics such as stress and
neighborhood preservation. We introduce a novel quality metric, cluster
distance preservation, to assess intermediate structure capture. All
source-code, datasets, experiments and analysis are available online.

通过可调参数，在图嵌入中实现局部和全局结构之间的平衡，以便在二维图上有效地捕捉局部和全局信息。使用综合质量指标评估了该方法的性能，结果表明其与最先进的方法竞争力相当，包括应力、邻域保持等。引入了一种新的质量指标用于评估中间结构的保持，所有的源代码、数据集、实验和分析结果都可以在线获取。

在图嵌入中平衡本地和全局结构（LGS）

Balancing between the Local and Global Structures (LGS) in Graph  Embedding

In this work, we addresses the problem of modeling distributions of graphs.
We introduce the Vector-Quantized Graph Auto-Encoder (VQ-GAE), a
permutation-equivariant discrete auto-encoder and designed to model the
distribution of graphs. By exploiting the permutation-equivariance of graph
neural networks (GNNs), our autoencoder circumvents the problem of the ordering
of the graph representation. We leverage the capability of GNNs to capture
local structures of graphs while employing vector-quantization to prevent the
mapping of discrete objects to a continuous latent space. Furthermore, the use
of autoregressive models enables us to capture the global structure of graphs
via the latent representation. We evaluate our model on standard datasets used
for graph generation and observe that it achieves excellent performance on some
of the most salient evaluation metrics compared to the state-of-the-art.

本文提出了一种基于图神经网络的离散自编码器，Vector-Quantized Graph Auto-Encoder (VQ-GAE)，用于模拟图的分布，通过利用图神经网络的等变性、局部结构和全局结构，以离散向量化的方式将图对象映射到潜在空间中捕捉整体结构，并在图形生成方面显示出优秀的性能。

向量量化图自编码器

Vector-Quantized Graph Auto-Encoder

In this paper, we propose one novel model for point cloud semantic
segmentation, which exploits both the local and global structures within the
point cloud based on the contextual point representations. Specifically, we
enrich each point representation by performing one novel gated fusion on the
point itself and its contextual points. Afterwards, based on the enriched
representation, we propose one novel graph pointnet module, relying on the
graph attention block to dynamically compose and update each point
representation within the local point cloud structure. Finally, we resort to
the spatial-wise and channel-wise attention strategies to exploit the point
cloud global structure and thereby yield the resulting semantic label for each
point. Extensive results on the public point cloud databases, namely the S3DIS
and ScanNet datasets, demonstrate the effectiveness of our proposed model,
outperforming the state-of-the-art approaches. Our code for this paper is
available at this https URL

本篇论文使用上下文点表示方法，提出了一种基于点云局部和全局结构的创新模型，使用门控融合和图形点网络模块进行语义分割，借助空间性和通道性的注意力策略，以 S3DIS 和 ScanNet 数据集为基础，效果超过现有最先进的方法。